document.write( "Question 738771: the hypotenuse of an isosceles right triangle is one meter longer than either of its legs. find the exact length of each side. \n" ); document.write( "

Algebra.Com's Answer #450912 by josmiceli(19441) $\"\"$ $\"About$

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If it's isosceles, then both legs are equal
\n" ); document.write( "Let $\"+x+\"$ = length of one of the legs
\n" ); document.write( " $\"+x%5E2+%2B+x%5E2+=+%28+x+%2B+1+%29%5E2+\"$
\n" ); document.write( " $\"+2x%5E2+=+x%5E2+%2B+2x+%2B+1+\"$
\n" ); document.write( " $\"+x%5E2+-+2x+-+1+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+-2+\"$
\n" ); document.write( " $\"+c+=+-1+\"$
\n" ); document.write( " $\"+x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2+-+4%2A1%2A%28-1%29+%29%29+%2F+%282%2A1%29+\"$
\n" ); document.write( " $\"+x+=+%28+2+%2B-+sqrt%28+4+%2B+4+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+x+=+%28+2+%2B-+sqrt%28+8+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+x+=+%28+2+%2B+2%2Asqrt%282%29+%29+%2F+2+\"$
\n" ); document.write( " $\"+x+=+1+%2B+sqrt%282%29+\"$ answer
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+2x%5E2+=+%28+x+%2B+1+%29%5E2+\"$
\n" ); document.write( " $\"+2%2A%28+1+%2B+sqrt%282%29+%29%5E2+=+%28+2+%2B+sqrt%282%29+%29%5E2+\"$
\n" ); document.write( " $\"+2%2A%28+1+%2B+2%2Asqrt%282%29+%2B+2+%29+=+4+%2B+4%2Asqrt%282%29+%2B+2+\"$
\n" ); document.write( " $\"+6+%2B+4%2Asqrt%282%29+=+6+%2B+4%2Asqrt%282%29+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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